CN100582828C - System and method for canceling disturbance in MEMS devices - Google Patents

System and method for canceling disturbance in MEMS devices Download PDF

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CN100582828C
CN100582828C CN200580019199A CN200580019199A CN100582828C CN 100582828 C CN100582828 C CN 100582828C CN 200580019199 A CN200580019199 A CN 200580019199A CN 200580019199 A CN200580019199 A CN 200580019199A CN 100582828 C CN100582828 C CN 100582828C
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catoptron
disturbance
control signals
feed
moving
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CN1977197A (en
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B·P·特雷迈恩
J·E·达维斯
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Capella Photonics Inc
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Capella Photonics Inc
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/35Optical coupling means having switching means
    • G02B6/3586Control or adjustment details, e.g. calibrating
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B26/00Optical devices or arrangements for the control of light using movable or deformable optical elements
    • G02B26/08Optical devices or arrangements for the control of light using movable or deformable optical elements for controlling the direction of light
    • G02B26/0816Optical devices or arrangements for the control of light using movable or deformable optical elements for controlling the direction of light by means of one or more reflecting elements
    • G02B26/0833Optical devices or arrangements for the control of light using movable or deformable optical elements for controlling the direction of light by means of one or more reflecting elements the reflecting element being a micromechanical device, e.g. a MEMS mirror, DMD
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/35Optical coupling means having switching means
    • G02B6/351Optical coupling means having switching means involving stationary waveguides with moving interposed optical elements
    • G02B6/3512Optical coupling means having switching means involving stationary waveguides with moving interposed optical elements the optical element being reflective, e.g. mirror
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/35Optical coupling means having switching means
    • G02B6/354Switching arrangements, i.e. number of input/output ports and interconnection types
    • G02B6/356Switching arrangements, i.e. number of input/output ports and interconnection types in an optical cross-connect device, e.g. routing and switching aspects of interconnecting different paths propagating different wavelengths to (re)configure the various input and output links
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/35Optical coupling means having switching means
    • G02B6/3586Control or adjustment details, e.g. calibrating
    • G02B6/3588Control or adjustment details, e.g. calibrating of the processed beams, i.e. controlling during switching of orientation, alignment, or beam propagation properties such as intensity, size or shape
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/35Optical coupling means having switching means
    • G02B6/3586Control or adjustment details, e.g. calibrating
    • G02B6/359Control or adjustment details, e.g. calibrating of the position of the moving element itself during switching, i.e. without monitoring the switched beams

Abstract

A system and method for canceling disturbance in a MEMS device. The system 200 includes a MEMS device 203, which may include a substrate 205 and a plurality of individually movable MEMS elements 203 - 1 through 203 -N, and a control assembly 207. The optical system 200 may be utilized in and/or form a portion of any optical apparatus employing an array of MEMS devices. The control assembly 207 uses feed-forward control signals to cancel disturbance in the MEMS device 203, and more particularly, to cancel disturbance in the non-switched or static mirrors of the MEMS device 203 caused by switched or moving mirrors.

Description

Be used for eliminating the system and method for MEMS device disturbance
Technical field
The present invention relates to MEMS (micro electro mechanical system) (MEMS).More particularly, the present invention relates to be used for eliminating the system and method for MEMS device (as the MEMS reflection mirror array) disturbance.
Background technology
MEMS device (as the MEMS catoptron) is effectively in various optical application, comprises that high-velocity scanning and optics switch.Shown in Fig. 1 is the optical system of prior art, and its use MEMS reflection mirror array will be from the output optical fibre that is optically coupled to of input optical fibre.Especially, Fig. 1 has described wavelength separated Route Selection (WSR) equipment 100, this equipment 100 comprises optical fiber collimator 110 arrays, wavelength-separation vessel, beam focusing device and MEMS device 103, described optical fiber collimator 110 provides one or more input and output ports (as port one 10-1 to 110-N), described wavelength-separation vessel a kind of can be diffraction grating 101 in form, described beam focusing device is the form of condenser lens 102, and described MEMS device 103 can be a micro reflector array.
In operating process, multiple-wavelength optical signals occurs from one or more input ports, as port one 10-1.Diffraction grating 101 is separated into multispectral passage by angle with multiple-wavelength optical signals.Each spectrum channel can represent that different centre wavelengths are (as λ i) with relevant bandwidth, and as in the WDM optical network applications, carrying unique information signal.Condenser lens 102 makes spectrum channel be focused into the space array (not shown in figure 1) of corresponding focal beam spot.Channel micromirrors 103 is located according to the space array that is formed by spectrum channel, so that each channel micromirrors is accepted spectrum channel one of them.Channel micromirrors 103 can be separately controlled and movably, under simulation (or continuously) control, be (or rotatable) that to pivot for example, so that be introduced into selected wherein some output ports (as port one 10-2 to 110-N) as condenser lens 102 and diffraction grating 101 at the reflex time spectrum channel.So, MEMS device 103 spectrum channel between the input and output port of this system that can be used to optionally to be coupled.System 100 also can comprise quarter-wave plate 104, and it causes the polarization of the total nearly 90 degree rotations of each spectrum channel experience when passing quarter-wave plate 104 twice.This and other examples of optical system of using MEMS device array (as micro-reflector) are at United States Patent(USP) Nos. 6,687, and 431,6,661,948,6,625,346 and 6, be described in 549,699, above-mentioned patent is transferred to this assignee and is combined in this by reference.
In the optical system of using the MEMS device, system as shown in Figure 1, the switching discrete component can cause the disturbance in the adjacent elements in the MEMS device.For example, in the MEMS array switched mirror find to cause with array in the aerodynamic force coupling of other catoptrons, this can upset and plan to keep static catoptron.Attempted to eliminate this disturbance in non-switching or the static mirrors.These effort concentrate on selects control strategy to reduce to minimum with this perturbation effect with the catoptron that is switched.For example, former work is included as switched mirror designing optimal track, and coupling system dynamics knowledge is so that reduce to minimum with disturbance.The U.S. Patent No. 5,668,680 of Tremaine has been discussed a kind of such solution.Other effort comprises the motion that slows down switched mirror, optimizes voltage and the time curve that produces mirror motion, and the blocking-up of the machinery between the cremasteric reflex mirror.
The invention provides the system and method for disturbance in a kind of MEMS of elimination device, its mode with the prevention perturbation is controlled the non-switching device in the MEMS device.
Summary of the invention
The invention provides the method and system that is used for eliminating the disturbance of MEMS device.The present invention utilizes Feed-forward Control Strategy to control non-switching device in the MEMS device, eliminates the perturbation that is caused by the switching device in the device effectively.In one embodiment, the MEMS device can be that MEMS reflection mirror array and control strategy can use traditional controller to realize.
According to one aspect of the present invention, provide optical system.Optical system comprises MEMS device and Control Component, described MEMS device comprises a plurality of elements, these elements are separately movably, described Control Component is communicatively coupled to the MEMS device and provides control signal to be used for moving meter to a plurality of elements, wherein said control signal comprises the feed-forward signal that is passed to some element, and it has eliminated the disturbance that is caused by moving meter basically.
According to another aspect of the present invention, the optical device that is used for eliminating the disturbance of MEMS reflection mirror array is provided, described MEMS catoptron is switchable separately.This equipment comprises controller, and described controller is communicatively coupled to the MFMS catoptron and feed-forward signal is passed to some catoptron, the disturbance that basic effectively elimination is caused by switched mirror.
According to another aspect of the present invention, the method that is used for eliminating the disturbance of MEMS device is provided, described MEMS device comprises a plurality of elements movably separately.This method comprises that the one or more elements in the MEMS device provide feed-forward signal, and described feed-forward signal has been eliminated the disturbance that is caused by the moving meter in the MEMS device effectively substantially.
Will be better understood novel feature of the present invention and invention itself according to following accompanying drawing and detailed description.
Description of drawings
Fig. 1 is the synoptic diagram according to the optical device of the use MEMS device array of prior art.
Fig. 2 is the synoptic diagram of explanation according to the optical device of the MEMS of comprising device array of the present invention.
Fig. 3 be in the explanation optical system mirror angle and be present in corresponding output port or the optically-coupled at collimating apparatus place between the typical optical coupled curve that concerns.
Fig. 4 has illustrated the example that can distribute with the DAC that the present invention uses.
Fig. 5 has illustrated the optical disturbance that comprises in the conventional optical systems of not utilizing MEMS device of the present invention.
Fig. 6 has illustrated the optical disturbance that comprises in the optical system of utilizing MEMS device of the present invention.
Embodiment
Describe the present invention referring now to accompanying drawing, described accompanying drawing be as illustrated example of the present invention provide so that enable those skilled in the art to implement the present invention.It should be noted that, as will being conspicuous concerning the those of ordinary skill of this neighborhood, the realization of some element of the present invention can use software, hardware, firmware or any wherein combination to finish, and accompanying drawing and following example do not plan to limit the scope of the invention.Utilizing known elements may partially or completely realize some element part of the present invention, only the part of understanding this known elements essential to the invention is described, and has omitted the detailed description of other parts of this known elements so that can not blur the present invention.The preferred embodiments of the present invention are illustrated in the accompanying drawings, and identical numeral is used to refer to the identical and corresponding part of various accompanying drawings.
In addition, represent the light beam of spectrum channel only to illustrate for purpose of explanation in the figure below the expression.For example, their size and dimension not drawn on scale.Should also be noted that in instructions, subscript i can be assumed between 1 and N between any round values.
Fig. 2 describes is partial view according to optical system 200 of the present invention.Optical system 200 comprises MEMS device 203, and it can comprise substrate 205 and a plurality of movably MEMS element 203-1 to 203-N and Control Component 207 separately.Optical system 200 can be used for and/or form the part of any optical device that uses the MEMS device array, the equipment described in any patent that lists above of equipment for example shown in Figure 1 or assignee.In one embodiment, MEMS element 203-1 to 203-N comprises micro-reflector (as the little machined mirrors of silicon), is similar to the micro-reflector that uses in optical system shown in Figure 1 100.In other embodiments, MEMS device 203 can comprise the pivotable, rotatable, switchable of any kind and/or optical element movably.In addition, the channel micromirrors of any number can be included in the array, and can be corresponding to the number of spectrum channel in the optical system.
Micro-reflector 203-1 to 203-N can be arranged to along the one-dimensional array of x-axle, and can be arranged in optical device so that receive the focal beam spot of the spectrum channel of apart correspondingly.Though micro-reflector shown in Figure 2 is the linear reflective lens array, the present invention also can be used for two-dimentional reflection mirror array or matrix.The reflecting surface of each micro-reflector as defined among the figure, be positioned at the x-y plane and be centered around the axis of rolling 212 that the x direction extends and the pitch axis 214 that extends in the y direction movably, such as being pivotable (or deflective).In simulation and/or digital control following, catoptron can be pivotable in a continuous manner.Each spectrum channel can be deflected with respect to its incident direction in the x and y direction at reflex time, so that be directed into the output port (the port one 10-2 in the system 100 as shown in Figure 1) in the optical system.Fig. 3 has illustrated the relation between the optically-coupled of corresponding output optical fibre in the angle of catoptron and reflecting bundle and the optical system.Although micro reflector array 203 has illustrated the MEMS catoptron with two turning axles, the present invention can be used for having the MEMS catoptron of any amount turning axle.In addition, though the description of present embodiment is relevant with the electrostatic MEMS catoptron, the present invention also can be used for utilizing the MEMS catoptron of other actuating methods (as voice coil motor or magnetostatics).
In one embodiment, Control Component 207 is included in the traditional controller function based on microprocessor under institute's program stored control.Controller can comprise the DSP firmware and the FPGA device of guiding Control Component 207 operations.In other embodiments, the hardware of other types, software and/or firmware can be used to realize the present invention.Control Component 207 provides one group of catoptron-control signal (as voltage signal U 1To U N), control micro-reflector 203-1 to 203-N moves.Utilize the changeable micro-reflector of DAC magnitude of voltage to instruct the corresponding anglec of rotation with this.For instance, the dashed rectangle among Fig. 2 220 has illustrated the diagrammatic side view of micro-reflector 203-i.In square frame 220, micro-reflector has experienced catoptron-control signal U i, and therefore with the angle θ that pivots iAround the rotation of x axle pivot (outer) by the paper plane sensing.
These catoptron control signals (as the DAC value) are control variable and will be by the symbol u of k catoptron in the linear array kRepresent.The perturbation that disturbance on the catoptron can be used as in the power level that records with dBm is observed by optical mode.Yet the disturbance of considering as output variable is catoptron angle of slip θ in the present embodiment kEven it is observed indirectly to by power level.
In operating process, Control Component 207 use feed-forward control signals are eliminated the disturbance in the MEMS device 203, and more particularly, eliminate the non-switching of MEMS device 203 or the disturbance in the static mirrors.Control Component 207 offers the catoptron (" reflector for switching ") that switches or move with standardization outline line f () with control signal, and it makes the coupling in the adjacent mirror (as the catoptron of relative next-door neighbour's switched mirror) reduce to minimum.Especially, Control Component 207 is suitable for utilizing control u kAt θ kAny two positions between mobile mirror k, simultaneously by means of to u jFeedforward control make θ jMinimum is reduced in middle transient response, wherein j ≠ k.In order to implement this function, Control Component 207 operations are as follows.If the difference between final value and the initial value is represented as Δ u k, then the control to switched mirror is u k=Δ u kF ().Although disturbance is reduced to minimum, adjacent mirror has the residual disturbance that available criteria function g () characterizes.
Experimental work and hydrodynamic force are calculated and have been shown that the disturbance on the adjacent mirror is proportional with the switched mirror speed and the switching anglec of rotation in the MEMS device.In addition, the kinetics equation of liquid stream is suitable in having the laminar flow scope of constant gas density.Reynolds number and Knudsen number are less than 1.These results advise that this system is linear and can uses stack.Utilize linear and the stack supposition, residual disturbance can be write as by u j=a JkΔ u kThe control u that g () provides jIn equivalent disturbance, a wherein JkBe defined as coupling coefficient from catoptron k to catoptron j.Control Component 207 provides Feed-forward Control Strategy, utilizes the additional control u of elimination from the disturbance of k catoptron with this j=-a JkΔ u kG () offsets equivalent disturbance control.Total feedforward control of j catoptron is the summation of all switched mirror,
u j=∑ all?k-a jk·Δu k·g(·),where?k?is?the?index?of?switched?mirrors?&?a kk=0
Disturbance slightly only influences adjacent catoptron (as the catoptron of relative next-door neighbour's switched mirror) rather than influences the entire emission lens array.Therefore, u jThe subclass of the only adjacent or static mirrors of calculating at all on be necessary or desired.For example, in one embodiment, Control Component 207 only consider near switched mirror adjacent+/-a N catoptron.The another kind of mode of stating this analysis is | coefficient a during j-k|>N Jk=0.The value of N can change based on the physical geometric of MEMS device.In one embodiment, N can equal 5.Can be with coefficient a JkCollect advance to have main diagonal line be zero and upper and lower five diagonal line be filled with the coupled matrix A of nonzero coefficient.Feedforward control then can be write as u=A Δ u kG ().Coupling coefficient can utilize automatic script to determine, by repeatedly switching each catoptron uses this device in proper order, utilizes the disturbance in the fluorescence detector measurement adjacent mirror with this simultaneously.Then regulate coupling coefficient a JkMake disturbance reduce to minimum with this.For each catoptron and neighbor thereof repeat this process, be filled into coupled matrix A until needed diagonal line.
Though present embodiment is applied to the axis of rolling with penalty function, in alternative embodiment, also another penalty function can be applied to pitch axis.
Feasibility of the present invention has obtained confirmation in including the optics path selection system Capella Photonics WavePath 4500 of micro reflector array.Fig. 5 and 6 is the example graph that confirm not use the result (Fig. 5) under the feedforward control situation and use the result (Fig. 6) under the feedforward control situation of the present invention.Fig. 4 has illustrated that the demonstration DAV that is used for two catoptrons distributes.In this case, catoptron 1 switches to the destination port from source port.Catoptron 1 is passed to destination port with this with wavelength separately at first in the rotation (curve 304) on the axis of rolling then of rotation (curve 302) on the pitch axis.Next, the optimum position is got back in pitch axis (curve 302) rotation.These DAC change corresponding with above-mentioned outline line f ().In this example, rotating (outline line 304) simultaneous on its axis of rolling with catoptron 1 is to utilize outline line g () (curve 306) to compensate by feed-forward control signals catoptron 2 around the disturbance from the aerodynamic force coupling of the axis of rolling.Other embodiment can be pitching and the rolling movement compensatory reflex mirror 2 and the adjacent catoptron of switched mirror.As illustrated in Figures 5 and 6, utilize the present invention to eliminate effectively or reduced disturbance (as 8.3dB to 0.5dB) on the non-switched mirror substantially.
Those of skill in the art recognize that above-mentioned example embodiment only provides several in the numerous optical systems that make up according to the present invention.Can design various mechanisms and method and implement the function of appointment in the mode of equivalence.In addition, under the situation that does not deviate from the principle of the invention and scope, can carry out various changes here, replace and select for use.Therefore, scope of the present invention should be determined by following claim and jural equivalent thereof.

Claims (34)

1. optical system comprises:
The MEMS device comprises movably a plurality of separately elements; And
Control Component, provide control signal to be used for moving described element with described MEMS device communicative couplings and to described a plurality of elements, wherein said control signal comprises the feed-forward control signals that is passed to some non-moving element, the disturbance that is caused by moving meter with basic elimination.
2. optical system as claimed in claim 1, wherein said a plurality of elements comprise micro-reflector.
3. optical system as claimed in claim 1, wherein said a plurality of elements are arranged to one-dimensional array.
4. optical system as claimed in claim 1, wherein said a plurality of elements are arranged to two-dimensional array.
5. optical system as claimed in claim 1, each of wherein said a plurality of elements is rotatable around at least one.
6. optical system as claimed in claim 1, each of wherein said a plurality of elements is rotatable around axle more than two.
7. optical system as claimed in claim 1, wherein said control signal comprise the DAC magnitude of voltage of corresponding rotation angle in the described element of instruction.
8. optical system as claimed in claim 1, wherein said some non-moving element comprises the element of the predetermined quantity adjacent with each side of moving meter.
9. optical system as claimed in claim 8, the element of wherein said predetermined quantity is based on the physical attribute of MEMS device.
10. optical system as claimed in claim 1, wherein said Control Component according under establish an equation and provide feed-forward control signals to non-moving element:
u j=∑-a jk·Δu k·g(·),
Wherein element k is a moving meter, u jBe the feed-forward control signals that is passed to non-moving element j, a JkBe coupling coefficient from element k to element j, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-moving element.
11. optical system as claimed in claim 10, wherein summation is carried out all k, and a Kk=0.
12. optical system as claimed in claim 11, wherein | a during j-k|>N Jk=0, wherein the value of N is based on the physical geometric of MEMS device and change.
13. optical system as claimed in claim 1, wherein said Control Component according under establish an equation and provide feed-forward control signals to non-moving element:
u=A·Δu k·g(·),
Wherein u is the feed-forward control signals that is passed to non-moving element, and A is the coupling coefficient matrix to non-moving element from moving meter, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-moving element.
14. an optical device that is used for eliminating the disturbance of MEMS reflection mirror array, described MEMS catoptron is switchable separately, and described equipment comprises:
Controller transmits feed-forward control signals with described MEMS catoptron communicative couplings and to some non-switched mirror, has eliminated the disturbance that is caused by switched mirror effectively substantially.
15. optical device as claimed in claim 14, wherein said catoptron is arranged to one-dimensional array.
16. optical device as claimed in claim 14, wherein said catoptron is arranged to two-dimensional array.
17. optical device as claimed in claim 14, each of wherein said catoptron is pivotable around at least one.
18. optical device as claimed in claim 14, each of wherein said catoptron is pivotable around axle more than two.
19. optical device as claimed in claim 14, its middle controller also provide control signal to switch the MEMS catoptron.
20. optical device as claimed in claim 19, wherein said control signal comprise the DAC magnitude of voltage of the corresponding anglec of rotation in the described catoptron of instruction.
21. optical device as claimed in claim 14, wherein said some non-switched mirror comprises the catoptron of the predetermined quantity adjacent with each side of switched mirror.
22. optical device as claimed in claim 21, the catoptron of wherein said predetermined quantity is based on the physical attribute of MEMS catoptron.
23. optical device as claimed in claim 14, wherein said controller according under establish an equation and provide feed-forward control signals to non-switched mirror:
u j=∑-a jk·Δu k·g(·),
Wherein catoptron k is a switched mirror, u jBe the feed-forward control signals that is passed to non-switched mirror j, a JkBe coupling coefficient from catoptron k to catoptron j, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-switched mirror.
24. optical device as claimed in claim 23, wherein summation is carried out all k, and a Kk=0.
25. optical device as claimed in claim 24, wherein | a during j-k|>N Jk=0, wherein the value of N is based on the physical geometric of MEMS device and change.
26. optical device as claimed in claim 14, wherein said controller according under establish an equation and provide feed-forward control signals to non-switched mirror:
u=A·Δu k·g(·),
Wherein u is the feed-forward control signals that is passed to non-switched mirror, and A is the coupling coefficient matrix of adaptive switched catoptron to non-switched mirror, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-switched mirror.
27. an elimination comprises the method for disturbance in the MEMS device of a plurality of elements, described a plurality of elements are separately movably, and described method comprises:
One or more non-moving element in described MEMS device provides feed-forward control signals, and described feed-forward control signals has been eliminated the disturbance that is caused by the moving meter in the described MEMS device effectively substantially.
28. method as claimed in claim 27, wherein said element comprises micro-reflector.
29. method as claimed in claim 27, wherein said one or more non-moving elements comprise the element of the predetermined quantity adjacent with each side of moving meter.
30. method as claimed in claim 29, the element of wherein said predetermined quantity is based on the physical attribute of MEMS device.
31. method as claimed in claim 27, wherein Control Component according under establish an equation and provide feed-forward control signals to non-moving element:
u j=∑-a jk·Δu k·g(·),
Wherein element k is a moving meter, u jBe the feed-forward control signals that is passed to non-moving element j, a JkBe coupling coefficient from element k to element j, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-moving element.
32. method as claimed in claim 31, wherein summation is carried out all k, and a Kk=0.
33. method as claimed in claim 32, wherein | a during j-k|>N Jk=0, wherein the value of N is based on the physical geometric of MEMS device and change.
34. method as claimed in claim 27, wherein Control Component according under establish an equation and provide feed-forward control signals to non-moving element:
u=A·Δu k·g(·),
Wherein u is the feed-forward control signals that is passed to non-moving element, and A is the coupling coefficient matrix to non-moving element from moving meter, Δ u kBe poor between final value and the initial value, and g () is the normalized function that characterizes disturbance in the non-moving element.
CN200580019199A 2004-04-16 2005-04-06 System and method for canceling disturbance in MEMS devices Expired - Fee Related CN100582828C (en)

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US6909819B1 (en) 2005-06-21
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